I do not advise making a cash down payment (i.e., cash cap reduction). A car is a depreciating asset and is purchased for consumption; and so, it's an expense and not an investment. No savvy investor would ever invest in stock that they know will depreciate or lose value over time. Also, if the vehicle is lost or stolen and never recovered, the insurance carrier will only pay ACV (actual cash value or est. market value). If your lease balance exceeds the ACV (called the GAP), your GAP protection will cover the difference. This GAP narrows the larger the down payment. Large down payments can cause the ACV to exceed the lease balance (negative GAP). In such cases, you necessarily risk losing part or all of your cap reduction if your car is totaled or stolen but never recovered.
It might be helpful to remember the following before deciding to make a cash down payment (i.e., cap cost reduction)...
If the GAP equals or exceeds 0, then you owe nothing and receive nothing. However, you've lost your entire cap reduction or down payment. The insurance company will pay the fund provider the ACV and the GAP carrier will pay the fund provider the difference between the amount owed (lease or loan balance) and the ACV. And so, the fund provider doesn't lose; you do!
If GAP < 0, then you'll receive, from the fund provider, the difference between the ACV and the lease balance or loan balance less any transaction costs incurred by the fund provider. However, this may not be sufficient to cover your cap reduction or down payment. In which case, you would lose the difference. The only thing the fund provider wants is the outstanding balance owed plus any transaction costs. You, of course, get whatever remains (the scraps so to speak).
One other thing... never buy GAP insurance from a dealer if the fund provider doesn't offer it in their lease contract, or provides it at additional charge, because the cost is inflated by about 1000%! Check with your insurance carrier and, whether you buy or lease, your carrier can attach a GAP rider to your existing insurance policy. The annual cost, as a rule of thumb, is roughly 0.1% of the vehicle's MSRP. So, if the MSRP is $49,000, then your annual GAP premium is roughly...
0.1% x $49,000 or about $49 annually.
John